I always thought that the value for Boltzmann's Constant was empirical (i.e. derived from experiment) however, due to the uncertainty factor of quantum mechanics this would seem a somewhat difficult task.

Note the following: The digits in parentheses are the uncertainty (standard deviation) in the last two digits of the measured value. In principle, the Boltzmann constant is a derived physical constant, as its value is determined by other physical constants. However, calculating the Boltzmann constant from first principles is far too complex to be done with current knowledge.

What the final part of this statement about 'current knowledge' indicates, I'm not quite sure, but it seems that Boltmann's Constant is indeed calculated from (or at least in part) a Mathematical model (based on the comment 'first principles')